MA17-03 Maths Coming soon
Estimating the Gradient of a Curve
MA17-03
This lesson is coming soon.
In this lesson
Estimate the gradient of a curved graph at a given point by drawing a tangent by eye and calculating its gradient, and interpret the result as a rate of change in context.
What it covers
- Drawing a tangent by eye to a curve at a specified point
- Choosing two clear points on the drawn tangent and calculating its gradient using rise over run
- Interpreting the resulting gradient value as a rate of change in the given context (e.g. speed at a moment in time from a distance-time curve, rate of reaction at a given time)
- Recognising why a tangent (not a chord, radius, or the point's own coordinates) is the correct construction for an instantaneous rate at a curved point
Key words
For: AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560, Edexcel IGCSE 4MA1, Cambridge IGCSE 0580
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | A15 | Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts |
| Edexcel GCSE 1MA1 | A15 | Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts (this does not include calculus) |
| Eduqas GCSE C300 | HA15 | Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts |
| OCR GCSE J560 | 7.04b | Understand the relationship between gradient and ratio. |
| Edexcel IGCSE 4MA1 | H3.3D | Find the gradients of non-linear graphs |
| Cambridge IGCSE 0580 | E2.9 | Use and interpret graphs in practical situations including travel graphs and conversion graphs. |
| Cambridge IGCSE 0580 | E2.12 | Estimate gradients of curves by drawing tangents. |
For teachers
This GCSE Maths lesson teaches estimating the gradient of a curve. By the end, students should be able to estimate the gradient of a curved graph at a given point by drawing a tangent by eye and calculating its gradient, and interpret the result as a rate of change in context. It works through two worked examples and the mistakes examiners report.